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I am in this peculiar position whereby I started off my grad school in subject X and got very boring projects in it and eventually around my 3rd year I started studying a new subject Y (partly because I met some inspiring profs in Y who motivated me)

Now in some sense it was just lucky that after about 6-7 months of working in this new field I along with another co-grad student hit upon a breakthrough research idea possibly solving a famous long-standing open question in this field Y! It was sheer luck that we hit upon an idea which seems to work! (though we are struggling hard to prove the theorem)

Now when I am trying to officially shift departments/institutes to pursue Y, I am explaining in my statements this new possible breakthrough that we hit upon. But I am a bit worried as to how senior established profs in Y will react seeing such a thing in my statement.


I think all answers till now are completely missing the point of this question and what I am worried about. So let me break-up the context in parts.

(1) In mathematical stuff no one wants to put on arxiv a "possible" method unless one has a rigorous proof for it to work. If we had a proof then I wouldn't be asking this question!

(2) In my SOP if I don't write about this progress then what else do I write about!? This is the main stuff that I have been working on ever since I decided to shift fields. So I don't see a choice but to write about this idea!

(3) The professors who have seen the idea seem to have no opinion at all. They take the view that unless there is a rigorous proof how do we know whether this is right or not. At this point all evidence is numerical simulations. (and the prof who originally inspired me to start Y remarked that he had himself independently also tried one of the ideas we came up with)

(4) I have anyway linked from my SOP a draft which explains the idea.

  • Are you planning to apply for another graduate school or stay at the current one? – scaaahu Aug 4 '15 at 8:32
  • Most probably trying to shift grad schools to pursue Y – RandomGrad Aug 4 '15 at 8:44
  • If you plan to stay at the current school, what do you mean by "explaining in my statements"? A research proposal? – scaaahu Aug 4 '15 at 8:47
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    If your breakthrough turned out to be unoriginal, or to have some fatal flaw, would you still want to switch to field Y? – Patricia Shanahan Aug 5 '15 at 6:37
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    No proof => no breakthrough. The fact that you have some heuristic that works for some cases, does not prove anything. You need to: a) Test with as many instances as possible b) Find a common pattern where your heuristic works for those instances where it works c) Based on that, find more problem instances where your heuristic works d) Describe where it does not work and why. e) Describe why it is useful to have a partial solution for working instances f) Give theoretical bounds where your instance would work and where it would not – Alexandros Aug 6 '15 at 7:39
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As a good researcher always be cautious with "breakthroughs". I would explain that you think it is a good idea worth pursuing. Coming off too strong may put new professors off. Unfortunately I have witnessed many times people believe they have come across breakthroughs when they are nothing of the sort. I think partly because unlike how science is portrayed in the media, "most" excellent science is a long grind, through years of experiments, thought, collaboration and trial and error. The road is often long and winding, and to approach someone well versed in the field with a "breakthrough" may be hubris. But, if it is a strong idea and worth pursuing with good reasoning/logic/science behind it, I cant see a problem convincing anybody in your field the importance of what you propose! Good luck!

  • This is precisely the risk that I am playing with. That we have made a progress in this big question in Y in 6 months of starting the subject is my argument for why I should be allowed to shift departments. But at the same time there is always the risk that may be everything is wrong. I don't know what is the solution to the dilemma. – RandomGrad Aug 4 '15 at 9:42
  • This progress that we think we have made is the crux of my argument in the SOP requesting the shift in departments/institutes. – RandomGrad Aug 4 '15 at 9:45
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    @RandomGrad There is no risk talking to the prof who motivated you to pursue Y. The most you lose is the time (6 months) you spent on it if the profs shows that your idea won't work. If he thinks the idea is fine, you get to go to his department and become his student. I don't see the problem talking to him before writing the statement unless there is something else you are worried about. – scaaahu Aug 4 '15 at 9:50
  • Its not about this one prof. I am asking about a generic grad application that I am now making to pursue the subject. (and no one can say that the idea won't work because all computer simulations show that it does work) – RandomGrad Aug 4 '15 at 15:36
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As I suggested in a comment, I think a key issue is whether your wish to switch to topic Y is conditional on the validity of your breakthrough. If it is, I agree with prior advice to document your priority on the idea and then start presenting it to professors as "Does this direction have any merit?".

If your wish to switch to topic Y is unconditional, there is an alternative strategy of delaying presenting your idea.

In order to have an opinion on the originality of your idea, you must have done a formidable amount of study of Y, including the history of attempts to solve the problem you are working on and related topics, despite the relatively short time you have been working on it. For purposes of an application SOP, you could present yourself as having become extremely interested in Y and wanting to do research in it.

That plan gives you a good chance of getting into Y research with no embarrassment if every serious, experienced Y researcher is already aware of flaws in your idea. It avoids the risk of being seen as a crank - the statistically most likely cause of an inexperienced researcher thinking they have a breakthrough on a long unsolved problem.

  • I have added more details into the question. Does any part of your answer change now? – RandomGrad Aug 6 '15 at 3:55
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    @RandomGrad No change, except the edits make it clear that you are working in an area in which proof is needed, and you don't have one. Given that, it is very, very important that you think through whether you want to switch to Y if the idea does not work out. – Patricia Shanahan Aug 6 '15 at 4:16
  • I don't see an obvious connection between wanting to shift to Y and this amazing project that I landed into. – RandomGrad Aug 6 '15 at 4:21
  • @RandomGrad I am confused. Obviously, this amazing project is connected to shift to Y if the project is in Y unless you want to be an independent researcher. Is there something we totally missed? – scaaahu Aug 6 '15 at 4:57
  • @RandomGrad I think you are putting too much weight on "this amazing project" and not enough weight on everything else. If your switch to Y is really a good idea you should be able to find enough to say in an SOP about why you should be a Y researcher independent of the one project. – Patricia Shanahan Aug 6 '15 at 9:08
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This is my advice,

You and your co-grad student write up your idea with your plan of attacking the solution and put it on arXiv. Then talk to the professors who motivated you to study subject Y to get their opinions. If the professors think you do have a possible breakthrough, ask them if you can shift to their department/school. If their answer is positive, start the formal application process.

I am not sure if you are worried that your idea could be stolen. This is why I suggest you to put it on arXiv first. Once it's on arXiv, that worry is gone. You should feel free to talk to the professors. If your idea is indeed workable, you have options.

You can stay in your current school/department so you won't waste your three years there. If you want to shift department or school, you'll have very strong recommendation letters from those professors because you already have possible breakthroughs.

You don't need to worry about the reactions from those professors. They are the experts in Y. They can tell if your idea is good after you present it. If it's not workable, you just lost six months of time and it's better you learn that fact before you waste even more time on it. If your idea is workable, they are going to be very happy because you have a breakthrough and you are their students.

Writing an SoP for the breakthrough at this moment may not be a good idea unless you are fairly certain that it is workable. Frankly, two graduate students spending 6 months to solve a famous long-standing open question is doubtful, but it is not unlikely. You do need experts to confirm it.

  • @scaahu I think everyone here is missing the issue totally! (1) In mathematical stuff no one wants to put on arxiv a "possible" method unless one has a rigorous proof for it to work. If we had a proof then I wouldn't be asking this question. (2) In my SOP if I don't wrote about this progress then what else do I write about!? This is the main stuff that I have been working on ever since I decided to shift fields. So I don't see a choice but to write about this idea! – RandomGrad Aug 6 '15 at 3:48
  • (3) The professors who have seen the idea seem to have no opinion at all. They take the view that unless there is a rigorous proof how do we know whether this is wrote or not. At this point all evidence is numerical simulations. – RandomGrad Aug 6 '15 at 3:50
  • @RandomGrad I am confused. In your question, you said "But I am a bit worried as to how senior established profs in Y will react seeing such a thing in my statement". Now, you say "The professors who have seen the idea seem to have no opinion at all". What exactly is your question? – scaaahu Aug 6 '15 at 3:55
  • I am talking of possible reaction from senior professors in an admission committee looking at my SOP. (the idea has been discussed at length with certain other professors I know : they think the observations are intriguing but they don't have an opinion if it will eventually work out : they think that any proof is going to be very hard given that there has been no progress till date ever till we suddenly came up with these ideas in the last few months) – RandomGrad Aug 6 '15 at 3:59

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